Allowing anonymous users to add items to SharePoint lists

​​​​​​To allow anonymous users to add items to a SharePoint list without giving them edit permissions to your site you can run the following PowerShell command.

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add-pssnapin microsoft.sharepoint.powershell

$siteurl = "[your site URL]"

$listname = "[your list name]"

$a = (get-spweb $siteurl).lists | where title -eq $listname

$a.AnonymousPermMask​64 = "ViewListItems, AddListItems, OpenItems, ViewVersions, ViewFormPages, Open, UseClientIntegration, UseRemoteAPIs"

Just enter the URL of you site and the name of the list in the appropriate values.